1 Introduction

Zinc-Aluminium (ZA) alloy is a potential candidate material due to its better strength, better castability and lower density of the ZA alloys for replacing brass, bronze to produce wear resistant parts and also general engineering applications [1,2,3,4]. The ZA alloys are used for production of numerous components hinge, bearings and small gears, earth moving equipment’s and cable winches [5,6,7]. Among the ZA alloys, ZA-27 alloy is a quite possibly recognized alloy with better strength and wear resistance significantly higher than that of a standard cast aluminium alloy [1].

One of the significant constraints of these alloys was the deterioration of mechanical and wear characteristics occur at operating temperature exceeds 100 °C [8, 9].

Many studies have been reported regarding the impact of the various alloying elements on wear properties of ZA alloys. In one of those studies, P Choudhary et al. [10] studied that the influence of nickel on the amount of wear response of ZA alloy. The results indicated that adding of Ni increases the amount of wear resistance of ZA alloy, due to the formation of intermetallic phases. Temel Savaskan et al. [11] considered the impact of silicon on the mechanical and wear characteristics of zinc-based alloy. The result reveals that hardness and strength of these alloys enhances with increased silicon content till 2 wt%, further it is diminished with increase in the content of silicon. It is likewise seen that coefficient of friction and wear loss of the alloy diminished with increased content of silicon till 2 wt% however above this level, the value increases. V Aleksandar et al. [12] examined the impact of strontium on the dry sliding wear behaviour of Zn25Al1Si alloys. The wear tests were performed with lubricated conditions using block on disc at room temperature. It was noticed that improvement in amount of wear and coefficient of friction with the addition of strontium but the coefficient of friction value was higher with increase in content of strontium. J P Pandey et al. [13] analysed the tribological wear behaviour under various operating parameters of zinc-based alloy. The wear performance of this alloy is also related through a leaded-tin bronze under same operating parameters. It was noticed that zinc-based alloy accomplishes better than leaded-tin bronze entire operating conditions. The predominant wear resistance of zinc-based alloy is due to effective lubricating and load bearing characteristics of its constituent phases.

By the previous survey of works, it is observed that more research work was done to improve the performance of zinc-aluminium alloy with varying parameters to determine wear resistance under dry sliding condition, and the studies were carried out by experiments only.

Artificial intelligence (AI) and machine learning (ML) approaches are being used in tribology to predict and optimize the tribological behaviour of various materials and operating conditions with numerous applications in mind, ranging from condition monitoring to the design of material compositions to lubricant formulations or film thickness predictions and friction behaviour in thermo-mechanical systems [14].

And also, it is observed that limited works has been carried out using machine learning (ML) techniques to understand the wear behaviour of zinc-aluminium alloy.

Out of a study, by Y Liu et al. [15] using artificial neural network, the trained model was more accurate and efficient in predicting hot deformation behaviour of ZA-27 alloy. In another study, by Osman Altay et al. [16] predicted the amount of wear for coated ferro-alloy using various machine learning techniques. Moosavin et al. [17] diagnosed the fault of journal-bearings of internal combustion engine using machine learning classifiers like artificial neural network and k-nearest neighbour.

In the current work, the prediction of wear loss of modified ZA-27 alloy under dry sliding condition was determined using machine learning algorithms namely interaction LR, the cubic kernel function of SVM, rational quadratic of GPR, KNN and RF.

2 Data Acquisition

In this work, wear tests were performed on modified ZA-27 alloy. The chemical composition of this alloy is shown in Table 1. Rockwell hardness testing machine was used to determine the hardness values of modified ZA-27 alloy.

Table 1 Chemical composition of modified ZA-27 alloy (wt%)
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Five successful measurements had been accomplished at a major load of 100 kg for 20 s with 2.5 mm diameter made of steel ball and to determine the specimen value of hardness, the average value was calculated as 81.86 HRB. The scanning electron microscope was used to understand the microstructure and EDS is performed to determine the chemical elements present in a modified ZA-27 alloy.

Figure 1a and b show the SEM and EDS of modified ZA-27 alloy, respectively. It consists of α phase (Al solid solution), β phase (Zn solid solution), ε phase (CuZn3) and intermetallic compounds such as Al–Mn.

Fig. 1
figure 1

SEM micrograph (a) and EDS (b) of modified ZA-27 alloy

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Dry sliding wear tests had been accomplished using friction and wear testing machine by varying operating parameters. The specimens used were 10 mm in diameter and 33 mm in length were cut using lathe machine. Before the tests, specimens were cleaned thoroughly by removing oil and dirt. Before each test, surface of each specimen and the disc are grounded using emery paper. At the end of each test, burrs are removed from faces of specimens to preserve flat surfaces. Wear test parameters which are used for this current work are listed in Table 2. The amount of wear loss of sample was weighed using an electronic microbalance (± 0.0001 g) [18]. The specimens wear losses at 4.905 N, 9.81, N, 19.62 N, 29.43 N and 39.24 N loads are represented in Figs. 2, 3, 4, 5 and 6.

Table 2 Wear test parameters
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Fig. 2
figure 2

Wear loss changes with sliding distance at 4.905 N

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Fig. 3
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Wear loss changes with sliding distance at 9.81 N

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Fig. 4
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Wear loss changes with sliding distance at 19.62 N

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Fig. 5
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Wear loss changes with sliding distance at 29.43 N

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Fig. 6
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Wear loss changes with sliding distance at 39.42 N

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The input parameters namely sliding distance, normal load and sliding speed [19] are used for training the machine learning algorithms. The experimental results of wear loss are considered as output parameter. Therefore, depend upon the input variables; the ML algorithm models predict the wear losses.

3 Machine Learning Algorithms

3.1 Linear Regression

The Regression model is used to build a functional relationship between dependent variable(s) and independent variable(s). Model’s data follows normal distribution and the line of best fit through the data points is a straight line.

Linear model between y and xi where i = 1,2, 3,…, n is expressed as [20]

$$ y = \beta_{o} + \beta_{1} x_{i} + \varepsilon $$
(1)

where y = predicted value of dependent variables, βo = y-intercept, β1 = Slope, ε = Error of the model.

The terms βo and β1 are the parameters of the models called as regression coefficients which can be determined as follows using Eqs. (2) and (3) [21].

$$\upbeta 1=\frac{{\sum }_{i=1}^{n}\left({x}_{i}-\overline{x }\right)\left({y}_{i}-\overline{y }\right)}{\sum_{i=1}^{n}{\left({x}_{i}-\overline{x }\right)}^{2}}$$
(2)
$$\mathrm{\beta o }=\overline{y }-{\upbeta }_{1}\overline{x }$$
(3)

where \(\overline{x }\) is the average of\({x}_{1}\),\({x}_{2}\),\({x}_{3}\),…, \({x}_{n} ,\) \(\overline{y }\) is the average of\({y}_{1}\),\({y}_{2}\),\({y}_{3}\),…, \({y}_{n}\), n is the sample size of independent variable.\(x\) is the independent variable (s) and \(y\) is the dependent variable(s). In this present work, we have used interaction linear regression.

3.2 Support Vector Machine

The SVM method was introduced by Vapnik and Chervonekis in 1992 to get the result for classification and regression problems [22]. According to the kernel function, there are several variations in SVM algorithm. The linear regression model in the SVM algorithm creates an association between output and input values [23]. In Eq. (4) \({y}_{i}\) denotes output sample, \({x}_{i}\) is the input sample, and \(a\) is the bias value, where \(w\) is the weight [24].

$${y}_{i}=\left({w}_{i}{x}_{i}\right)+a$$
(4)

In current work of SVM algorithm, the kernel function is used as a quadratic loss function which is as follows [24].

$${L}_{\text{quad}}\left(f\left(x\right)-y\right)={\left(f\left(x\right)-y\right)}^{2}$$
(5)

The optimized results were found by the above equation. The above equation is made easier with Karush–Kuhn–Tucker (KKT) conditions, in Eqs. (6) and (7) [24, 25]

$${}_{\beta }{}^{\text{min}}.\frac{1}{2}\sum_{i=1}^{l}\sum_{i=1}^{l}{\beta }_{i}{\beta }_{j}\left({x}_{i}{x}_{j}\right)-\sum_{i=1}^{l}{\beta }_{i}{y}_{i}+\frac{1}{2C}\sum_{i=1}^{l}{{\beta }_{i}}^{2}$$
(6)
$$\overline{\alpha }\overline{\alpha }=0, i=1,\dots ,l$$
(7)

With constraints

$$\sum_{i=1}^{l}{\beta }_{i}=0, i=1,\dots ,l$$
(8)

The below equation gives the Cubic kernel function [24]

$$K\left(x,y\right)=1+xy+{\text{min}}\left(x,y\right)-\frac{\left(x+y\right)}{2}{\left({\text{min}}\left(x,y\right)\right)}^{2}+\frac{1}{3}{\left({\text{min}}\left(x,y\right)\right)}^{3}$$
(9)

The below equation gives the regression function [24]

$$\overline{w }=\sum_{i=1}^{l}{\overline{\beta }}_{i}{x}_{i}\stackrel{-}{, b}=-\frac{1}{2}\overline{w }\left[{x}_{r}+{x}_{s}\right]$$
(10)

3.3 Gaussian Process Regression

GPR is a supervised machine learning approach that interpolates observations by proposing and testing a large number of probabilistic prediction functions. GPR can work with minimal data sets, unlike many supervised techniques. It will also produce a distribution for the expected values, which can be converted into empirical confidence intervals for the prediction [26].

Let the vector \({x}_{n}\) represent a specific location in the input field. \({x}_{n}\equiv {\left\{{x}^{n}\right\}}_{n=1}^{N}\) be the set of training input vectors \({y}_{n}\equiv {\left\{{y}^{n}\right\}}_{n=1}^{N}\) be the target vectors. The mean covariance (Kernel) function can fully explain the Gaussian process \(f(x)\). These functions are given independently, and include a functional form definition as well as collection of hyper parameters. The mean function is utilised to describe value of expected function at any position in input fields before training data are evaluated. The equation of mean function is [27]

$$m\left(x\right)=E(f\left(x\right))$$
(11)

Similarity concept is an elementary assumption that points with similar inputs \(x\) will likely have similar y target output, so the training near another point of testing may be relevant in terms of the prediction at that point. The covariance function defines proximity or likeness in Gaussian processes. The covariance function of two functional values were estimated at fixed points x and \({x}^{^{\prime}}\) is written as [27]

$$k\left(x,{x}^{^{\prime}}\right)=E\left[\left(f\left(x\right)-m\left(x\right)\right)\left(f\left({x}^{^{\prime}}\right)-m\left(x\right)\right)\right]$$
(12)

Knowing the covariance function allows you to deduce one function value from the other. As a result, the covariance function \(k(x,{x}^{^{\prime}})\) can be read as the distance between the input points \(x\) and \({x}^{^{\prime}}\).

As a result, the Gaussian process may be written as follows [27]:

$$f\left(x\right)\sim GP\left[m\left(x\right),k(x,{x}^{^{\prime}})\right]$$
(13)

The zero mean function is as follows for all \(x\) values:

$$m\left(x\right)=0$$
(14)

In this work, rational quadratic kernel function is used and equation is written as [28]

$${k}_{R{\text{Qard}}}\left(x,{x}^{^{\prime}}\right)= {\sigma }_{f}^{2}{\left(1+\frac{1}{2\alpha {l}^{2}}{\left(x-{x}^{^{\prime}}\right)}^{T }\left(x-{x}^{^{\prime}}\right)\right)}^{-\alpha }$$
(15)

where α is the rational quadratic covariance's shape parameter.

3.4 Random Forest

In 2001, Leo Breiman created the random forest (RF) approach. RF is a supervised learning algorithm contains multiple decision trees. RF is used for both classification and regression problems [29].

The subgroups are separated from the source set based on value attribute tests likewise a tree can be trained. The act of repeating this procedure on each derived subset is known as recursive partitioning. The recursion completes when the splitting no longer.

A tree can be "trained" by separating the source set into subgroups depending on attribute value checks. The act of repeating this procedure on each derived subset is known as recursive partitioning. The recursion terminates when every node of the subsets has the same target variable value, or when splitting is no more necessary to get the predictions [30].

The training data set is used to establish the properties each of the forest's decision trees, as well as the nodes inside each decision tree. Regression findings, on the other hand, are stored in leaves. Experiments are used to calculate the number of trees in a forest.

Bootstrap methods are used to determine the new training data sets for each tree by utilising the set of experimental data with input parameters (x) likely sliding distance, normal load and sliding speed and output parameter (y) as wear volume loss D = (x, y).

The most significant properties of each node are then determined. After creating the trees, the set of predictable values for test data are calculated to determine the method's correctness.

Linear regression is based on a model that looks like this:

$$f\left(X\right)={\beta }_{0}+\sum_{j=1}^{p}{X}_{j}{\beta }_{j}$$
(16)

Regression trees, on the other hand, are based on a model of the kind

$$f\left(X\right)= \sum_{m=1}^{M}{c}_{m}.1(X\in {R}_{m})$$
(17)

where R1,…,Rm denotes a feature space division [31].

3.5 K-Nearest Neighbor (KNN)

The KNN algorithm become an effective technique to carry out discriminant analysis while the dependable parametric estimation of opportunity densities changes into unknown or too difficult to determine. The KNN algorithm turned into typically based totally at the Euclidean distance (\({d}_{i}\)) among testing samples and the specified training samples [32].

$${d}_{i}=\sqrt{{\left({x}_{l1}-{x}_{m1}\right)}^{2}+{\left({x}_{l2}-{x}_{m2}\right)}^{2}+. . . + {\left({x}_{ln}-{x}_{ms}\right)}^{2}}$$
(18)

where \({x}_{l}\) was an input sample with n features, n was the total number of input samples and n was the total number of input features [33].

The KNN equation for the regression is [34]

$$\widehat{y}\left(x\right)= \frac{1}{k} \sum {x}_{i}\epsilon N\left(x\right){y}_{i}$$
(19)

where N(x) is the set for nearest neighbors. We choose k, how many nearest neighbors are taken into consideration to calculate the prediction, and k corresponding y is summed up. It’s far divided using k. To sum up, it simply offers the average of the y-value of the nearest neighbors.

4 Results and Discussion

4.1 Wear Prediction by Machine Learning Algorithms

The current work was planned to find the wear loss of modified ZA-27 alloy by the gravity die casting method. We have applied machine learning algorithms like GPR, SVM, RF, KNN and LR to predict the wear loss by considering three inputs like sliding distance, normal load and sliding speed while wear loss as output. The data set collected by the experiment was divided into 30% test data and 70% training data. The function of rational quadratic is used in GPR algorithm, In SVM algorithm we used cubic kernel function, Bagging technique is used in RF regression and interaction function is applied in LR algorithm. To construct the effective models k-fold cross-validation procedure was adopted with fold value of 10, and with three evaluative criteria like mean absolute error (MAE) and Root Mean Square Error (RMSE) and R2 [27].

$$\mathrm{MAE}=\frac{1}{n}\sum_{i}^{n}\left|{y}_{i}-{x}_{i}\right|$$
(20)

where \(n\) is number of data points, \({y}_{i}\) is prediction and \({x}_{i}\) is true value.

$$\mathrm{RMSE}=\sqrt{\frac{1}{n}\sum_{i=1}^{n}{\left(\frac{{y}_{i-{Y}_{i}}}{{Y}_{i}}\right)}^{2}}$$
(21)

where n is the sample points, \({y}_{i}\) is the predictive value and \({Y}_{i}\) is the experimental value.

$${R}^{2}=1-\frac{{\sum_{i}\left({s}_{i}-{\widehat{s}}_{i}\right)}^{2}}{{\sum_{i}\left({s}_{i}-{\overline{s} }_{i}\right)}^{2}}$$
(22)

where \(s\) is variable to be predicted, \(\widehat{s}\) is the predicted value and \(\overline{s }\) is total variability in s.

Initially all the supervised machine learning algorithms are trained with both input features (normal load, sliding speed and sliding distance) and output label (wear loss). Later the model predictions are made from the trained samples with reference to the regression analysis by assessing the data and fitting a hyperplane (straight line) in the following criteria:

LR fits the model with minimum sum of mean-squared error for respective data points. In GPR, prediction is made by calculating the probability distribution for all the admissible functions which fits the data. SVM fits the model based on maximum data points over the hyperplane. In KNN, prediction is made on the bases of feature similarities by calculating the distance (Euclidean) between the data points. In RF, prediction of the model is made by considering the average results of the multiple decision trees.

It was noticed that, the predicted R2 (training) values are 0.987, 0.903, 0.848, 0.809 and 0.753 was attained in the RF, GPR, KNN, SVM, and LR, respectively. The predicted R2 (test) values are 0.943, 0.866, 0.761, 0.771, and 0.745 was attained in the RF, GPR, KNN, SVM, and LR, respectively. Out of the constructed models, RF has yielded the superior predicted R2 values in training and testing, MAE and RMSE. The calculated resultant values are accessible in Table 3. All the machine learning algorithms used in this work were self-scripted using python programming language in Spyder IDE.

Table 3 Models performance in prediction of wear loss
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The Random Forest, which is composed of several decision trees. Our data are divided into smaller subsets by the algorithm. The end result is a tree with leaf nodes and decision nodes. The value of each feature (such as normal load, sliding speed, and sliding distance) examined is represented by two or more branches in a decision node, and the outcome is stored in the leaf node (target value). A single decision tree's failure to correctly anticipate the target value is eliminated using many decision trees. As a result, the random forest averages the results from numerous trees to arrive at the final result.

Hence, random forest has given highest accuracy rate compared to the other algorithms.

The predicted and experimented values of constructed models are given away in Fig. 7. We could observe that, the predicted values of the constructed models are pretty closer to the experimented values. All the constructed models (LR, SVM, GPR, RF and KNN) analysis graphs are depicted in Fig. 8.

Fig. 7
figure 7

Experimental and predicted wear losses

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Fig. 8
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Regression analysis graphs

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Many manufacturing industries which produce wear resistant components are used in agricultural machinery, automotive industry and engineering applications faces certain burdens like manpower, experimentation time and cost of production that could be improved by adopting our proposed model.

4.2 Worn Surface Morphology

By adding the Mn in the ZA-27 alloy it strengthened the phase in solid solution. Also it strengthens the inter-dendritic binary of ternary eutectic phases and resists the migration of grain boundary. Also Mn can be refined the Al phase.

From Fig. 9 it is observed the smooth worn out surface at 1.5 m/s sliding velocity and applied load of 19.62 N. Very low amount of wearing surface is deformed plastically and smaller material removal patches are observed on the wearing surface. Hence, minimum wear rate is observed. The corresponding thin flattened debris surface is observed in Fig. 10.

Fig. 9
figure 9

Worn surface SEM micro graph of 0.52% Mn as received specimen at Speed-1.5 m/s and 19.62 N load

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Fig. 10
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Wear debris of 0.52% Mn as received specimen at Speed-1.5 m/s and 19.62 N load

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From Fig. 11 it is observed that with increasing the normal pressure for the specimens with 0.52% Mn content there is increase in volumetric wear rate. With increase in the normal pressure actual metal contacting area between the sample and its counterpart is large hence results in more volumetric wear rate. For the specimen 0.52% Mn, under the high speed of 2.5 m/s but under high normal load of 39.24 N, the surface is more smeared Fig. 11 and the smeared almost flattened debris with some oxidative surface is observed Fig. 12.

Fig. 11
figure 11

Worn surface SEM micro graph of 0.52% Mn as received specimen at 2.5 m/s sliding speed and 39.24 N applied normal load

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Fig. 12
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Wear debris of 0.52% Mn as received specimen at 2.5 m/s sliding speed and 39.24 N applied normal load

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5 Conclusions

In prediction of wear behaviour of modified ZA-27 alloy ML techniques were adopted. The constructed models have been predicted the wear loss using supervised machine learning algorithms such as LR, SVM, GPR, RF and KNN was observed.

  1. 1.

    By adopting the proposed model, we may expect the improvements in the manpower, experimentation time and cost of production.

  2. 2.

    In comparison with all the constructed models, the performance rate of RF was pretty higher and LR was lower, with respect to R2 values in training and testing, MAE and RMSE for the prediction of wear loss.

  3. 3.

    Sliding velocity and applied load impacted the wear behavior of modified ZA27 alloy, at higher loads and speeds there was more wear loss and was justified by worn surfaces and wear debris.